Advertisement

Computational Experience with Hypergraph-Based Methods for Automatic Decomposition in Discrete Optimization

  • Jiadong Wang
  • Ted Ralphs
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7874)

Abstract

Branch-and-price (BAP) algorithms based on Dantzig-Wolfe decomposition have shown great success in solving mixed integer linear optimization problems (MILPs) with specific identifiable structure. Only recently has there been investigation into the development of a “generic” version of BAP for unstructured MILPs. One of the most important elements required for such a generic BAP algorithm is an automatic method of decomposition. In this paper, we report on preliminary experiments using hypergraph partitioning as a means of performing such automatic decomposition.

Keywords

Block Structure Column Generation Integer Variable Restricted Master Problem Block Increase 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Catalyurek, U.V., Aykanat, C.: Hypergraph-partitioning-based decomposition for parallel sparse-matrix vector multiplication. IEEE Transactions on Parallel and Distributed Systems 10, 673–693 (1999)CrossRefGoogle Scholar
  2. 2.
    Bergner, M., Caprara, A., Ceselli, A., Furini, F., Lübbecke, M.E., Malaguti, E., Traversi, E.: Automatic Dantzig-Wolfe reformulation of mixed integer programs, http://www.optimization-online.org/DB_FILE/2012/09/3614.pdf
  3. 3.
    Gamrath, G., Lübbecke, M.E.: Experiments with a generic Dantzig-Wolfe decomposition for integer programs. In: Festa, P. (ed.) SEA 2010. LNCS, vol. 6049, pp. 239–252. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    Ralphs, T.K., Galati, M.V.: DIP (2012), https://projects.coin-or.org/Dip
  5. 5.
    Wang, J., Ralphs, T.K.: Computational experience with hypergraph-based methods for automatic decomposition in integer programming. Technical Report 12T-014, COR@L Laboratory, Lehigh University (2012), http://coral.ie.lehigh.edu/~ted/files/papers/CPAIOR12.pdf
  6. 6.
    Barnhart, C., Johnson, E.L., Nemhauser, G.L., Savelsbergh, M.W.P., Vance, P.H.: Branch-and-price: Column generation for solving huge integer programs. Operations Research 46, 316–329 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Galati, M.V.: Decomposition in Integer Programming. PhD thesis, Lehigh University (2009), http://coral.ie.lehigh.edu/~ted/files/papers/MatthewGalatiDissertation09.pdf
  8. 8.
    Vanderbeck, F.: BaPCod–a generic branch-and-price code (2005), http://wiki.bordeaux.inria.fr/realopt
  9. 9.
    Ladányi, L.: BCP: Branch-cut-price framework (2012), https://projects.coin-or.org/Bcp
  10. 10.
    Jünger, M., Thienel, S.: The ABACUS system for branch and cut and price algorithms in integer programming and combinatorial optimization. Software Practice and Experience 30, 1325–1352 (2001)CrossRefGoogle Scholar
  11. 11.
    Borndörfer, R., Ferreira, C.E., Martin, A.: Decomposing matrices into blocks. SIAM Journal on Optimization 9, 236–269 (1998)zbMATHCrossRefGoogle Scholar
  12. 12.
    Ferris, M., Horn, J.: Partitioning mathematical programs for parallel solution. Mathematical Programming 80, 35–61 (1998)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Catalyürek, U.V., Aykanat, C.: PaToH: A multilevel hypergraph partitioning tool, version 3.0. Technical Report 6533, Bilkent University, Department of Computer Engineering (1999)Google Scholar
  14. 14.
    Aykanat, C., Pinar, A., Çatalyürek, Ü.V.: Permuting sparse rectangular matrices into block-diagonal form. SIAM Journal on Scientific Computing 25, 1860–1879 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Achterberg, T., Koch, T., Martin, A.: The mixed integer programming library: MIPLIB 2003 (2003), http://miplib.zib.de/miplib2003
  16. 16.
    Karypis, G., Kumar, V.: hMETIS 1.5: A hypergraph partitioning package. Technical report, Department of Computer Science, University of Minnesota (1998), http://www.cs.umn.edu/metis
  17. 17.
    Çatalyürek, Ü.V., Aykanat, C.: PaToH: partitioning tool for hypergraphs (2012), http://bmi.osu.edu/~umit/software.html
  18. 18.
    Forrest, J.J.: CLP: COIN-OR linear Programming Solver (2012), https://projects.coin-or.org/Clp
  19. 19.
    Forrest, J.J.: CBC: COIN-OR branch-and-cut solver (2012), https://projects.coin-or.org/Cbc
  20. 20.
    Koch, T., Achterberg, T., Andersen, E., Bastert, O., Berthold, T., Bixby, R.E., Danna, E., Gamrath, G., Gleixner, A.M., Heinz, S., et al.: MIPLIB 2010. Mathematical Programming Computation 3, 103–163 (2011)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jiadong Wang
    • 1
  • Ted Ralphs
    • 1
  1. 1.Department of Industrial and Systems EngineeringLehigh UniversityUSA

Personalised recommendations